# Electromagnetics (`geobrain.physics.em`)

The electromagnetic family, galvanic through inductive, in one module.

| Method | Operators |
|---|---|
| DC resistivity | `DC2D`, `DC25D`, `DC3D` |
| Induced polarization | `IP2D`, `IP3D`, `IPSimulator`, `IPChargeabilityModel` |
| Spectral IP | `SIP`, `SIPColeColeModel` |
| Magnetotellurics | `MT1D`, `MT2D`, `MT3D` |
| Frequency-domain EM | `FDEM3D`, `FDEMCyl`, `HEM`, `VTEM` |
| Time-domain EM | `TEM1D`, `TEM3D`, `WaveformTEM1D` |
| Controlled source | `CSEM1D` |
| Self potential | `SelfPotential2D` |

Each has its own survey type (`DC2DSurvey`, `MT1DSurvey`, `FDEM3DSurvey`,
`TEM1DSurvey` and the rest), and the electrode, loop or station geometry lives
there rather than in the operator, so one operator serves many acquisitions.
`DipoleDipoleSurvey` and `BoundDipoleDipoleSurvey` build the standard arrays.

`Conductivity`, `Resistivity`, `Permittivity` and `Permeability` wrap the
physical properties; `ComplexData`, `FieldComponent` and `TimeWaveform`
describe what comes back.

## Before you run one

**Topography is not decoration.** The standard treatment is to let the mesh
continue above the ground, give the cells above the surface the conductivity of
air, and drape the electrodes onto the first ground cell in each column.
Nothing about the operator changes: the air is just very resistive rock. But
the air cells must be **held fixed** during inversion: their gradient is the
largest in the model, because a tiny conductivity in the denominator makes the
objective extremely sensitive there, and inverting them fills the sky with
current.

**Apparent chargeability is a ratio of two solves.** It is
`(V_eta - V_inf) / V_eta`, so the dipole difference has to be taken on each
potential *separately*, before the ratio is formed. Differencing apparent
chargeability between receivers is not a thing you may do.

**Chargeability is bounded.** It lives in `[0, 1)`, so it is inverted through a
sigmoid rather than as a free parameter: an unbounded step drives the effective
conductivity `sigma_inf (1 - eta)` negative and the solve fails. The starting
model matters too. Start at `eta = 0.2` everywhere and the optimizer sits
there; start near zero and it finds the body.

```{figure} /_figures/02_dc_resistivity.png
:class: gb-tall
:alt: A DC survey over topography, inverted

A DC survey over topography, inverted until chi-squared reaches 1. From
`examples/03_physics/02_dc_resistivity.py`.
```

## Stopping

Data carry noise, so a model that drives the misfit to zero is fitting noise
and will grow structure to do it. The EM examples watch chi-squared, the
misfit in units of the noise, and stop at 1, which is the statistically
honest place to stop, and it is a rule rather than an iteration count.

## See also

- `examples/03_physics/02_dc_resistivity.py`: a survey over a ridge, and
  chi-squared as the stopping rule.
- `examples/03_physics/03_induced_polarization.py`: the image resistivity
  cannot give you.
- `examples/03_physics/05_em_induction.py`: one airborne sounding, four
  decades of frequency, a layered earth read back out.